商务统计学Ch12PPT学习教案

1、会计学1商务统计学商务统计学Ch12Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-2第1页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-3n第2页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-4第3页/共74页Business Statistics: A First Course, 5

2、e 2009 Prentice-Hall, Inc.Chap 12-5第4页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-6YXYXYYXX线性相关线性相关曲线相关曲线相关第5页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-7YXYXYYXX强相关强相关弱相关弱相关(续)第6页/共74页Business Statistics: A First Course, 5e 2009 Pre

3、ntice-Hall, Inc.Chap 12-8YXYX不相关不相关(续)第7页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-9ii10iXY线性组成部分总体的 Y轴截距总体的斜率 随机误差项因变量自变量随机误差部分第8页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-10(续)取值Xi时，因变量的随机误差YX与Xi对应的Y的观测值与Xi 对应的Y的预测值ii10iXYXi斜率 =

4、 1截距 0 i第9页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-11i10iXbbY一元线性回归方程可以估计总体回归直线回归截距的估计值回归斜率的估计值第i个观测值的Y的估计（预测）值第 i个观测值X的值第10页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-122i10i2ii)Xb(b(Ymin)Y(YminY第11页/共74页Business Statistics: A F

5、irst Course, 5e 2009 Prentice-Hall, Inc.Chap 12-13文章中为感兴趣的读者列出了公式第12页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-14第13页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-15第14页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall,

6、Inc.Chap 12-16房价房价(1000美元）美元）(Y)平方英尺平方英尺 (X)2451400312160027917003081875199110021915504052350324245031914252551700第15页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-17第16页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-18第17页/共74页Business St

7、atistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-19Regression StatisticsMultiple R0.76211R Square0.58082Adjusted R Square0.52842Standard Error41.33032Observations10ANOVA dfSSMSFSignificance FRegression118934.934818934.934811.08480.01039Residual813665.56521708.1957Total932600.5000 Coeffic

8、ientsStandard Errort StatP-valueLower 95%Upper 95%Intercept98.2483358.033481.692960.12892-35.57720232.07386Square Feet0.109770.032973.329380.010390.033740.18580回归方程为: 98.24833 0.10977 ()房价平方英尺第18页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-20The regression equation i

9、sPrice = 98.2 + 0.110 Square Feet Predictor Coef SE Coef T PConstant 98.25 58.03 1.69 0.129Square Feet 0.10977 0.03297 3.33 0.010 S = 41.3303 R-Sq = 58.1% R-Sq(adj) = 52.8% Analysis of Variance Source DF SS MS F PRegression 1 18935 18935 11.08 0.010Residual Error 8 13666 1708Total 9 32600回归方程为:房价 =

10、98.24833 + 0.10977 (平方英尺)第19页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-21 98.24833 0.10977 ()房价平方英尺斜率 = 0.10977截距= 98.248 第20页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-22 98.24833 0.10977 ()房价平方英尺第21页/共74页Business Statistics: A Fi

11、rst Course, 5e 2009 Prentice-Hall, Inc.Chap 12-23 98.24833 0.10977 ()房价平方英尺第22页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-24 98.25 0.1098 ()98.25 0.1098(2000)317.85房价平方英尺预测有2000平方英尺的房子的价格:一个有2000平方英尺的房子的预测价格是317.85(1,000美元) = 317,850美元第23页/共74页Business Statistics: A

12、 First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-25相关范围内插值不要试图推断超出观测X的相关范围的房价第24页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-26SSE SSR SST总平方和回归平方和残差平方和2i)YY(SST2ii)YY(SSE2i)YY(SSR其中: = 因变量的均值Yi = 因变量的观测值 = 与Xi 对应的Y的观测值iYY第25页/共74页Business Statistics: A First Course

13、, 5e 2009 Prentice-Hall, Inc.Chap 12-27(续)第26页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-28(续)XiYXYiSST = (Yi - Y)2SSE = (Yi - Yi )2 SSR = (Yi - Y)2 _Y YY_Y 第27页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-291r02注意:2 SSRrSST回归平方和总平方和第

14、28页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-30r2 = 1YXYXr2 = 1r2 = 1X 和和 Y是强线性关系是强线性关系: 100% 的的Y的离差可以由的离差可以由 X的离差来解释的离差来解释第29页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-31YXYX0 r2 1X 和和 Y之间是弱线性关系之间是弱线性关系: 一部分但并不是所有的一部分但并不是所有的Y的离差都

15、可以用的离差都可以用X的离差可以解释的离差可以解释第30页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-32r2 = 0X 和和 Y之间没有线性关系之间没有线性关系: Y 的值不依赖于的值不依赖于X. (Y的离差不能用的离差不能用X的离差解释的离差解释)YXr2 = 0第31页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-33Regression StatisticsMultipl

16、e R0.76211R Square0.58082Adjusted R Square0.52842Standard Error41.33032Observations10ANOVA dfSSMSFSignificance FRegression118934.934818934.934811.08480.01039Residual813665.56521708.1957Total932600.5000 CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept98.2483358.033481.692960.12892-3

17、5.57720232.07386Square Feet0.109770.032973.329380.010390.033740.1858058.08%的房价离差可以由平方英尺的离差来解释0.5808232600.500018934.9348SSTSSRr2第32页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-34The regression equation isPrice = 98.2 + 0.110 Square Feet Predictor Coef SE Coef T PCons

18、tant 98.25 58.03 1.69 0.129Square Feet 0.10977 0.03297 3.33 0.010 S = 41.3303 R-Sq = 58.1% R-Sq(adj) = 52.8% Analysis of Variance Source DF SS MS F PRegression 1 18935 18935 11.08 0.010Residual Error 8 13666 1708Total 9 326000.5808232600.500018934.9348SSTSSRr258.08%的房价离差可以有平方英尺的离差来解释第33页/共74页Busines

19、s Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-352)(212nYYnSSESniiiYX其中SSE = 残差平方和 n = 样本量第34页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-36Regression StatisticsMultiple R0.76211R Square0.58082Adjusted R Square0.52842Standard Error41.33032Observatio

20、ns10ANOVA dfSSMSFSignificance FRegression118934.934818934.934811.08480.01039Residual813665.56521708.1957Total932600.5000 CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept98.2483358.033481.692960.12892-35.57720232.07386Square Feet0.109770.032973.329380.010390.033740.1858041.33032SYX第

21、35页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-37The regression equation isPrice = 98.2 + 0.110 Square Feet Predictor Coef SE Coef T PConstant 98.25 58.03 1.69 0.129Square Feet 0.10977 0.03297 3.33 0.010 S = 41.3303 R-Sq = 58.1% R-Sq(adj) = 52.8% Analysis of Variance

22、 Source DF SS MS F PRegression 1 18935 18935 11.08 0.010Residual Error 8 13666 1708Total 9 3260041.33032SYX第36页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-38YYXXSYX小 SYX大SYX表示Y的观测值偏离回归线的程度SYX的 大小应该是相对于样本数据中Y值的大小而言的例如,相对于房价在200000美元-400000美元的范围 SYX = $41.33K 比较小第37页/共

23、74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-39n误差项所服从分布的方差为常数第38页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-40n残差的图形分析n可以画出残差随X的变化图iiiYYe第39页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-41非线性非线性线性线性x残差xY

24、xYx残差第40页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-42检验独立性的残差分析不独立不独立独立独立XX残差残差X残差第41页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-43第42页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-44百分率百分率残差残差当使用正态概率

25、图时, 正态误差大约将会排列在一条直线上-3 -2 -1 0 1 2 30100第43页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-45不同方差同方差xxYxxYresidualsresiduals第44页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-46残差输出预测的房价 残差1251.92316-6.9231622273.8767138.123293284.85348-5.8

26、534844304.062843.9371625218.99284-19.992846268.38832-49.388327356.2025148.797498367.17929-43.179299254.667464.3326410284.85348-29.85348没有违背任何回归假设第45页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-472iYXYXb)X(XSSSXSS1其中:= 斜率标准差的估计值 = 这个估计值的标准差1bS2nSSESYX第46页/共74页Business

27、 Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-481b11STATSbt2nd.f.其中: b1 = 回归斜率系数 1 = 斜率假定值 Sb1 = 样本斜率的标准差第47页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-49房价（1000）(y)平方英尺 (x)2451400312160027917003081875199110021915504052350324245031914252551700 98.2

28、5 0.1098 ()房价平方英尺估计的回归方程估计的回归方程:这个模型的斜率 0.1098 房价与房子建筑面积（平方英尺）有关系吗？第48页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-50来自来自 Excel 的输出的输出: CoefficientsStandard Errort StatP-valueIntercept98.2483358.033481.692960.12892Square Feet0.109770.032973.329380.010391bSb1329383032

29、9700109770Sbt1b11STAT.Predictor Coef SE Coef T PConstant 98.25 58.03 1.69 0.129Square Feet 0.10977 0.03297 3.33 0.010来自来自 Minitab 的输出的输出: b11bS第49页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-51检验统计量: tSTAT = 3.329有足够的证据表明建筑面积影响房价决策: 拒绝 H0拒绝 H0拒绝 H0a/2=.025-t/2不拒绝 H00

30、t/2a/2=.025-2.30602.30603.329d.f. = 10- 2 = 8第50页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-52来自来自 Excel输出输出 : CoefficientsStandard Errort StatP-valueIntercept98.2483358.033481.692960.12892Square Feet0.109770.032973.329380.01039p-值有足够的证据表明建筑面积影响房价.决策: 拒绝 H0, 因为 p-值

31、Predictor Coef SE Coef T PConstant 98.25 58.03 1.69 0.129Square Feet 0.10977 0.03297 3.33 0.010来自来自 Minitab输出输出: 第51页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-53MSEMSRFSTAT21nSSEMSESSRMSR其中 FSTAT 服从自由度为1和 (n 2)的F 分布第52页/共74页Business Statistics: A First Course, 5e 2

32、009 Prentice-Hall, Inc.Chap 12-54Regression StatisticsMultiple R0.76211R Square0.58082Adjusted R Square0.52842Standard Error41.33032Observations10ANOVA dfSSMSFSignificance FRegression118934.934818934.934811.08480.01039Residual813665.56521708.1957Total932600.5000 11.08481708.195718934.9348MSEMSRFSTAT

33、自由度为自由度为1和和8F检验的检验的p-值值第53页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-55Analysis of Variance Source DF SS MS F PRegression 1 18935 18935 11.08 0.010Residual Error 8 13666 1708Total 9 3260011.08481708.195718934.9348MSEMSRFSTAT自由度为自由度为1和和8F检验的检验的p-值值第54页/共74页Business

34、Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-56检验统计量检验统计量: 决策决策:结论结论:拒绝 H0 ，在显著性水平 a a = 0.05的 情况下有足够的证据表明房子的大小影响销售价格0 a = .05F.05 = 5.32拒绝 H0不拒绝 H011.08FSTATMSEMSR临界值临界值: Fa a = 5.32(续)F第55页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-57斜率置信区间的估计:房价

35、的Excel打印输出:在 95%的置信水平下， 斜率的置信区间为 (0.0337, 0.1858)1b2/1Sbt CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept98.2483358.033481.692960.12892-35.57720232.07386Square Feet0.109770.032973.329380.010390.033740.18580d.f. = n - 2第56页/共74页Business Statistics: A First Course, 5e 2009 Prentice-

36、Hall, Inc.Chap 12-58由于变量房价的变化单元为1000美元，我们有 95% 的把握保证，每平方英尺的建筑面积对销售价格的影响在33.74美元到185.8美元之间 CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept98.2483358.033481.692960.12892-35.57720232.07386Square Feet0.109770.032973.329380.010390.033740.18580 95% 的置信区间 不包括 0.结论: 在0.05的显著性水平下，房价与平方英尺的关

37、系是显著的(续)第57页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-592nr1-rt2STAT2121 b 0 b 0rrrr 如果如果其中第58页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-60在.05的显著性水平下，有证据显示平方英尺与房价是线性关系吗？H0: = 0 (不相关)H1: 0 (相关) a =.05 , df = 10 - 2 = 83.329210.762

38、10.7622nr1rt22STAT(续)第59页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-61结论结论:在在5%的显著性水平下，有证据表明存在线性关系的显著性水平下，有证据表明存在线性关系决策决策:拒绝 H0拒绝 H0拒绝 H0a/2=.025-t/2不拒绝 H00t/2a/2=.025-2.30602.30603.329d.f. = 10-2 = 83.329210.76210.7622nr1rt22STAT(续)第60页/共74页Business Statistics: A F

39、irst Course, 5e 2009 Prentice-Hall, Inc.Chap 12-62YX XiY = b0+b1Xi 给定Xi，Y 均值的置信区间给定Xi, 单个Y值的预测区间目标: 对于给定的Xi， 形成因变量均值的置信区间表示对其值的不确定Y 第61页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-63给定特定的Xi，估计 Y 均值的置信区间区间的大小取决于与均值X的距离iY|X X/2YX : SiYtha的置信区间2i2i2ii)X(X)X(Xn1SSX)X(Xn1h第62页/共74页Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.Chap 12-64给定特定的Xi，估计单个因变量Y的预测值区间为了反映单个个别事件的不确定性，将区间宽度增加一项额外项iX X/2YXY: S1iYtha的预测区间为第63页/共74页Business Statistics: A First Course, 5e 2009 Prent